Topology optimization for lightweight cellular material and structure simultaneously by combining SIMP with BESO

This paper presents a hybrid algorithm for topology optimization of lightweight cellular materials and structures simultaneously by combining solid isotropic material with penalization (SIMP) and bi-directional evolutionary structural optimization (BESO). Microstructure of the lightweight cellular material is assumed unique in the structure to make the proposed method feasible. A new sensitivity analysis formula with respect to the discrete variable is derived by a principal submatrix stiffness matrix, by which the material can be effectively removed from or added to cellular. Moreover, the validity of the proposed method is then demonstrated through two numerical examples (a simple supported beam and a cantilever beam), which can be easily applied in a variety of practical situations.